Fractional Quantum Hall Edge Electrons, Chiral Anomaly and the Berry Phase

TL;DR

This paper explains deviations from universal power-law correlations in fractional quantum Hall edge states by analyzing chiral anomaly and Berry phase effects, revealing nonlocality in electron operators and linking edge excitations to bulk polarization states.

Contribution

It introduces a framework connecting chiral anomaly and Berry phase to edge electron correlations, explaining deviations from universal exponents and classifying edge modes by polarization states.

Findings

Deviation from universal power-law exponent explained by nonlocal electron operators.

Edge excitations are described by chiral boson fields with branch numbers related to polarization.

The number of edge branches varies with filling factor and spin polarization.

Abstract

It is shown that the deviation of fractional quantum Hall edge fluid from power law correlation functions with universal exponent $\alpha=1/\nu$ as observed in recent experiment may be explained when analyzed from the viewpoint of chiral anomaly and Berry phase. It is observed that at the edge anomaly vanishes and this induces a nonlocal effect in the construction of the electron creation operator in terms of the edge boson fields. This nonlocality is responsible for the deviation of the power law exponent from $\alpha=1/\nu$ of the edge fluid. There are gapless edge excitations described by chiral boson fields and the number of branches of chiral boson fields can be related to the polarization states of electrons in the bulk. We have noted that for fully polarized state at $\nu=\frac{1}{2m \pm 1}$ we will have a single branch whereas for partially polarized state at $\nu=\frac{n}{2mn \pm 1}$, with $n >1$ and odd, we will have $n$ branches. However for unpolarized state at $\nu=\frac{n}{2mn \pm 1}$ with $n$ even we will have two branches.